When i try to do pushups, i feel a sharp pain in my elbows and shoulders like they are on the verge of breaking, is this a calcium deficiency?

Unlikely: If you feel pain when performing pushups, this is more likely an issue with your joints or tendons, and not due to calcium deficiency -- a thorough exam from your primary care doctor would be very helpful.

Agree with Dr. C.: You should try less strenuous exercises to build muscle strength before resuming push ups. It is good that you are exercising. Have a healthy diet, drink plenty of water, avoid alcohol and street drugs, exercise at least 150 minutes per week. Wish you good health.